Monks P D D, Connor J N L, Althorpe S C
School of Chemistry, The University of Manchester, Manchester M13 9PL, England.
J Phys Chem A. 2006 Jan 19;110(2):741-8. doi: 10.1021/jp0556254.
Nearside-farside (NF) theory, originally developed in the energy domain for the time-independent description of molecular collisions and chemical reactions, is applied to the plane wave packet (PWP) formulation of time-dependent scattering. The NF theory decomposes the partial wave series representation for the time-dependent PWP scattering amplitude into two time-dependent subamplitudes: one N, the other F. In addition, NF local angular momentum (LAM) theory is applied to the PWP scattering amplitude. The novel concept of a cumulative time-evolving differential cross section is introduced, in which the upper infinite time limit of a half-Fourier transform is replaced by a finite time. In a similar way, a cumulative energy-evolving angular distribution is defined. Application is made to the state-to-state reaction, H + D2(v(i) = 0, j(i) = 0) --> HD(v(f) = 3, j(f) = 0) + D, where v(i), j(i) and v(f), j(f) are vibrational and rotational quantum numbers for the initial and final states, respectively. This reaction exhibits time-direct and time-delayed (by about 25 fs) collision mechanisms. It is shown that the direct-time mechanism is N dominant scattering, whereas the time-delayed mechanism exhibits characteristics of NF interference. The NF and LAM theories provide valuable insights into the time-dependent properties of a reaction, as do snapshots from a movie of the cumulative time-evolving differential cross section.
近侧-远侧（NF）理论最初是在能量领域为分子碰撞和化学反应的定态描述而发展起来的，现被应用于含时散射的平面波包（PWP）公式中。NF理论将含时PWP散射振幅的分波级数表示分解为两个含时子振幅：一个是N，另一个是F。此外，NF局部角动量（LAM）理论也被应用于PWP散射振幅。引入了累积时间演化微分截面的新概念，其中半傅里叶变换的上无穷时间极限被一个有限时间所取代。以类似的方式，定义了累积能量演化角分布。将其应用于态-态反应H + D2（v(i) = 0，j(i) = 零）→HD（v(f) = 3，j(f) = 0）+ D，其中v(i)、j(i)和v(f)、j(f)分别是初态和末态的振动和转动量子数。该反应呈现出时间直接和时间延迟（约25飞秒）的碰撞机制。结果表明，直接时间机制是N主导散射，而时间延迟机制呈现出NF干涉的特征。NF和LAM理论为反应的含时性质提供了有价值的见解，累积时间演化微分截面的电影快照也是如此。
